Question

a. Consider a (spherical) pebble of radius 1 cm falling under the influence of gravity. Assume it experiences a quadratic drag force (i.e., proportional to the velocity squared). Assume the constant of proportionality for the drag force is the product of a constant κQ and a geometric factor is the square of the radius. Assume the density of stone is 2500 kg/m3 and that κQ = 0.87 kg/m3 . Estimate the terminal velocity of the pebble (vT ). b. Consider the microscopic spherical droplet of oil (of radius r) moving under the influence of gravity that R.A. Millikan used to determine the elementary electric charge. The oil droplet fell vertically between two parallel plates. Before turning on the voltage between the two plates (so to create a uniform electric field in between), Millikan measured the terminal velocity of the drop (vT ) and compared to theory to estimate the drop radius. He assumed the drop experiences a linear drag force (i.e., proportional to the velocity). Assume the constant of proportionality for the drag force (FD) is the product of a constant κL and a geometric factor that goes as the radius (i.e., FD = κLr). Further, assume the density of oil is 800 kg/m3 , κL = 3.1 × 10−4 kg/m·s), and the drop radius is one micron. Estimate vT .

Answer 1